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Bounds on a regression coefficient under omitted-variable bias

Source: R/api.R
regsen_bounds.Rd

Computes the identified set for the coefficient on the primary independent variable in the infeasible long regression, across a grid of sensitivity parameters. Implements the analyses of Diegert, Masten & Poirier (2026) (the default) and of Oster (2019) extended by Masten & Poirier (2026).

Usage

regsen_bounds(
  formula,
  data,
  analysis = c("dmp", "oster"),
  compare = NULL,
  nocompare = NULL,
  rxbar = NULL,
  rybar = Inf,
  cbar = 1,
  clow = 0,
  rybar_expr = NULL,
  delta = NULL,
  r2long = 1,
  maxovb = NA,
  delta_type = c("eq", "bound"),
  r2long_type = c("eq", "relative"),
  maxovb_type = c("bound", "relative"),
  beta = "sign",
  product = TRUE,
  subset = NULL,
  ncores = NULL
)

Arguments

formula

Two-sided formula: y ~ x + w1 + w2 + .... The first right-hand-side variable is the primary independent variable; the rest are controls.

data

A data.frame.

analysis

Which sensitivity analysis to run: "dmp" (default) or "oster".

compare

Optional character vector of variables to use as the comparison set. Defaults to all controls if neither compare nor nocompare is given.

nocompare

Optional character vector of controls to exclude from the comparison set.

rxbar, rybar, cbar

(DMP) Numeric vectors of sensitivity-parameter values to sweep over. rybar = Inf (the default) gives the no-rybar case; setting it finite invokes the global-optimization code path.

clow

(DMP) Lower bound on control endogeneity, the clow of DMP Assumption A6 R(W2 ~ W1 . W0) %in% [clow, cbar]. Default 0, which asserts nothing beyond cbar. A positive value asserts that the controls are at least that endogenous. Must satisfy 0 <= clow <= min(cbar).

rybar_expr

(DMP) A function function(rxbar) rybar to set rybar as a function of rxbar (the only supported form in the Stata source is rybar = rxbar, i.e. function(rxbar) rxbar).

delta, r2long, maxovb

(Oster) Numeric vectors of sensitivity values.

delta_type

One of "eq" (equality, the default) or "bound".

r2long_type

One of "eq" (the default) or "relative". When "relative", values are multiplied by R-squared(medium).

maxovb_type

One of "bound" (default) or "relative". When "relative", values are multiplied by |Beta(medium)|.

beta

Hypothesis spec for the breakdown point. See regsen_breakdown().

product

Logical. If TRUE (default), all combinations of the sensitivity-parameter grids are evaluated; if FALSE, the inputs are zipped element-wise. Maps to Stata's noproduct option (inverted).

subset

Optional logical or integer vector indicating which rows of data to include in the estimation.

ncores

Number of cores to spread the grid over. NULL (default) uses the session setting of regsen_cores(), which is 1 unless changed; "auto" uses all but two of the machine's cores. Only the finite-rybar regime is costly enough to benefit. Results are identical for any number of cores.

Value

A regsensitivity object. The results field holds a data.frame with one row per sensitivity-parameter point.

For a breakdown analysis, results$breakdown is signed: its sign carries the direction of selection, and for Oster it is the delta that solves Proposition 3 for the hypothesised value. Feeding that value back into regsen_bounds() recovers the hypothesised beta, but feeding abs() of it lands on a different branch of the cubic. The scalar $breakdown field and the print method report the magnitude, since that is what is quoted as "the breakdown point". Note that the scalar exists on regsen_bounds() output only; a regsen_breakdown() result carries the value in results$breakdown alone.

Examples

data(bfg2020)
bnds <- regsen_bounds(
  avgrep2000to2016 ~ tye_tfe890_500kNI_100_l6 +
    log_area_2010 + lat + lon + temp_mean + rain_mean + elev_mean +
    d_coa + d_riv + d_lak + ave_gyi,
  data = bfg2020,
  cbar = 0.1
)
print(bnds)
#> 
#> Regression Sensitivity Analysis ----- Bounds
#> ------------------------------------------------------------------------
#> Analysis:          DMP (2026)
#> Treatment:         tye_tfe890_500kNI_100_l6
#> Outcome:           avgrep2000to2016
#> N (obs):           2036
#> Hypothesis:        Beta > 0
#> Breakdown point:   0.3726
#> 
#> --- Summary statistics ----------------------------------
#>   Beta (short)                  1.7078
#>   Beta (medium)                 1.5864
#>   R2 (short)                    0.0269
#>   R2 (medium)                   0.1345
#>   Var(Y)                      136.3204
#>   Var(X)                        1.2574
#>   Var(X_Residual)               1.0903
#> 
#> --- Results ---------------------------------------------
#>    rxbar rybar   cbar     bmin   bmax
#>        0  +Inf    0.1   1.5864 1.5864
#>  0.20427  +Inf    0.1   0.7386 2.4343
#>  0.40855  +Inf    0.1 -0.16388 3.3368
#>  0.61282  +Inf    0.1  -1.1489 4.3218
#>   0.8171  +Inf    0.1  -2.2576 5.4304
#>   1.0214  +Inf    0.1  -3.5556 6.7285
#>   1.2256  +Inf    0.1  -5.1601  8.333
#>   1.4299  +Inf    0.1  -7.3101 10.483
#>   1.6342  +Inf    0.1  -10.614 13.786
#>   1.8385  +Inf    0.1  -17.445 20.618
#>   2.0427  +Inf    0.1     -Inf   +Inf